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AVERAGE WORTH AND SIMULTANEOUS ESTIMATION OF

THE SELECTED SUBSET

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P. VELLAISAMY

*Department of Mathematics, Indian Institute of Technology, Powai, Bombay - 400 076, India*
(Received February 6, 1990; revised March 7, 1991)

**Abstract.**
Suppose a subset of populations is selected from the
given *k*
gamma *G*(*theta*_{i},*p*) (*i* = 1,2,....,*k*) populations, using Gupta's rule (1963,
*ninit Ann. Inst. Statist. Math.*, **14**, 199-216). The problem of
estimating the average worth of the selected subset is first considered.
The natural
estimator is shown to be positively biased and the UMVUE is obtained using
Robbins'
UV method of estimation (1988, *Statistical Decision Theory and Related
Topics IV, Vol.* 1 (eds. S. S. Gupta and J. O. Berger), 265-270, Springer, New
York). A class of estimators that dominate the natural estimator for an
arbitrary
*k* is derived. Similar results are observed for the simultaneous
estimation of the
selected subset.

*Key words and phrases*:
Gamma populations, subset selection,
estimation
after subset selection, average worth, natural estimator, UMVUE,
inadmissibility,
simultaneous estimation after selection.

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